STXB385

FACULTY WORKINGPAPER NO. 1517

Monopsony, Factor Prices, and Community Development

Lanny Arvan

Leon N. Moses

College of Commerce and Business Administration

Bureau of Economic and Business ResearchUniversity of Illinois, Urbana-Champaign

i

BEBR

FACULTY WORKING PAPER NO. 1517

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

November 1988

Monopsony, Factor Prices, and Community Development

Lanny Arvan, Associate ProfessorDepartment of Economics

Leon N. MosesNorthwestern University

Digitized by the Internet Archive

in 2011 with funding from

University of Illinois Urbana-Champaign

http://www.archive.org/details/monopsonyfactorp1517arva

MONOPSONY, FACTOR PRICES, AND COMMUNITY DEVELOPMENTby

y yLanny Arvan* and Leon N. Moses

Abstract

We consider a simple general equilibrium model of the effects on

local development and factor price determination from the entry of a large

export oriented firm into a small community. The large firm has monopsony

power but is not a pure monopsonist in that it must compete with a local

service sector and an already situated export sector for its factor demands.

Each of these sectors are taken to be comprised of many small firms which

act as price takers in both the factor and product markets. Moreover, the

factor supply functions are general equilibrium in nature in that the price of

other factors as well as the price of local services act as determinants of

factor supply. We present an extensive example where we compute the

local general equilibrium and where we derive a community indirect utility

function which allows us to contrast the developmental effects under the

hypothesis that the large firm acts strategically In the factor markets with

the hypothesis that the large firm acts as a price taker. We conclude the

paper with a brief discussion of an intertemporal version of our model,

where the large firm, having superior access to the (nonlocal) capital

market, is motivated In part by a desire to capture arbitrage profit in the

land market. The intertemporal version appears to produce a more realistic

view of factor price determination than what emerges from static analysis.

Associate Professor of Economics, University of Illinois at Urbana-Champaign;

**Professor of Economics and of Management, Northwestern University.

i

MONOPSONY, FACTOR PRICES, AND COMMUNITY DEVELOPMENT

by

Lanny Arvan* and Leon N. Moses

I. Introduction

This paper examines the developmental and factor price effects of

entry by a large, export oriented firm into a small community. The size of

the firm relative to that of the community is such that the firm's rate of

output and Its choice of Input combinations influence the prices it must pay

for local factors of production, land and labor. Because the firm has

monopsonistic power It adopts a profit maximizing strategy that involves

strategic quantity setting in the local factor markets.

The model used to examine these developmental and factor price

effects has two main characteristics. First, it is general equilibrium in

character It deals with the impact on the output, factor usage, and price of

a local goods and service sector from the large firm's entry into the

community. It also Investigates the effect the large firm has on the output

and employment of an existing export sector that, like the local goods

sector, is made up of firms that-'OPe-'atcmtst'iC'tnrboth their input^aml^utptrt

markets. The second characteristic of the model derives from the fact that

the large firm is not a pure monopsonist. it is dominant in local factor

markets but It Is not the exclusive employer, even after all of the effects of

entry by the large firm have been worked out and the community is In a new

long run equilibrium. In both respects the model Is a departure and

generalization of the traditional partial equilibrium monopsony model.

*Assoclate Professor of Economics, University of Illinois at Urbana-Champaign;

**Professor of Economics and of Management, Northwestern University.

Sor far as we have been able to determine, there has been little work

done on extending the partial equilibrium approach In this manner. Two

exceptions are Bunting ( 1 962) and Stratton ( 1 985). Bunting performs a cross

sectional study to analyze the Impact of firm concentration on wages. He

finds that the anticipated negative sign of the firm size coefficient Is

absent. Indeed In most cases the coefficient Is not statistically significant.

Stratton reaches the opposite conclusion while working with a different

data set. A theoretical model which considers a dominant firm In a local

labor market has been advanced by Richards ( 1 983). However, his model Is

flawed In that he assumes the firms which comprise the competitive fringe

In the demand for labor have a perfectly elastic labor demand function. This

either rules out monopsony power by the large firm or rules out operation

of the competitive fringe.

In considering the impact of a large new firm on the development of a

small community the necessity to take account of general equilibrium

effects should be readily apparent. First, factor supply functions, in

general, depend on the prices of other factors as well as on the prices of

final prnduda^^nce entry by the large firm will affect these prices, the

large firm's behaviour can be thought of as shifting the partial equilibrium

factor supply function. As this shifting effect is not usually considered in

partial equilibrium analysis, such an analysis is incomplete. Second, the

factor demand function by the competitive fringe also depends on the prices

of other factors and the product prices of the firms constituting the

competitive fringe. The same caveat regarding curve shifting applies here

as well.

Regional scientists, economists, and planners have always been very

—mucti concerned with the Impacts of new Industry on communities and

regions. There Is a massive body of literature on regional and Interregional

Input-output and regional complex analysis that deals with such Impacts and

to which Isard ( 1 95 1 . 1 953. 1 965) has been a major contributor. Economic

base and regional multiplier models also directly address the issue of direct

and Indirect employment, and sometimes even land use effects of entry Into

an area of a new Industry. A fine summary of this literature Is provided by

Richardson (1985). An Important critique of local multiplier studies has

been given by Merrifield (1987). He points out that economic base theory

suffers from an unrealistic and unpalatable factor supply assumption;

factor supply functions, including that of land, are perfectly elastic. He

argues for the introduction of supply side constraints into such analyses.

There Is also a body of literature that deals directly with the question

of the different effects of entry by a large as against entry by a number of

small businesses into a community. For example Bowles (1982) in a study of

Appalachia finds that large absentee firms explains much of the area's

poverty. An approacbJto iQcal-Ctevelopment favoring the attraction of small

business known as the "Incubator approach" has received considerable

attention in the literature. ' Basquero (1987) in a study of the development

of local development in Spain contrasts the growth of indigenous small

firms to the entry by large firms which leave major centers of industrial

agglomeration to seek the factor price advantages of peripheral areas and

^ See Temalj and Can(tece( 1984). Small Towns ( 1985. 1986. 1987). Somers( 1986), Brower.

Pollard, and Propst( 1 986), and Thomas ( 1 986) who deal with the special problems of

development in small towns.

finds that much of the development of small zones in Spain resulted from

growth of the fonrrerr"'^"'^''^^

Regional scientists do not appear to have had a great deal of interest

In modeling the large versus small firm issues in development. The regional

science literature does contain an immense amount of scholarly work

dealing with spatial problems of monopoly that arise on the product side.

Here one must mention the recent, all inclusive and immensely impressive

volume by Greenhut, Norman, and Hung (1987). However, we are unaware of

any comparable treatment which deals explicitly with departures from

perfect competition on the factor side.

The welfare Impacts of monopsony has been given some treatment in

the international trade literature. This work has been pioneered by

Feenstra (1980). McCulloch and Yellen (1980). and Markussen and Robson

(1980). Further work particulary interestested in the development of

multinationals has been done by Mendez ( 1 984) and Markussen ( 1 984).

Because these papers adopt the Hecksher-Ohlin assumption that factor

supplies are perfectly inelastic they are really incapable of examining the

developmeatal ancLXactor price effecta-of monopsony, the concern of our

paper.

II. A Static Model of Fntry by a Big Firm into a Small Community

H. I Setup of the Cieneral Framework

We consider a model of a small isolated community in which a large

firm plans to locate. The community's assets are its endowments of two

factors of production, land and labor, and its endowment of the numeraire 2

Prior to the entry of the largrflrm'thTcommuniti) has a small Industry

devoted to export to the rest of the country and a sector which produces

services that are consumed locally. It is assumed that both the export and

local goods sector operate under constant returns to scale. The proceeds

from export are spent on imports of commodities which are not locally

produced. Both the export and import prices are set on national markets vis

a vis which the local producers act as price takers. There is a third input

which is required in production, capital. The price of capital is also set on a

national market. In the short run the capital Input in both the export and

local goods sector Is fixed and the associated fixed costs constitutes a

liability for the community. In the long run each sector treats all Inputs as

variable.

The consumers in the community have preferences defined over

consumption of final goods; the export good, the import good, and the locally

produced good; as well as land and leisure consumption. Capital is not

consumed. It is assumed that each consumer has preferences which can be

represented by the same homothetic utilitity function. This assumption is

made for aggregation purposes. In what follows we will consider the

demand functions of the single aggregate consumer.

Let X| denote the export good, X2 the import good, x-^ the locally

produced good, K capital, L land, and N labor. Let the respective prices be

pj, ^2' P3> f^' ^' 3^^ W- P|> P2' ^^^ ^ ^^^ ^^^^^ ^^'^^ ^^^ P^^^^ ^^ ^^^^ ^^ ^^^

2 We assume that some of the community's endowment is held tn a commodity which is traded with

the rest of the country rather than assume that the entire endowment consists of land and labor

.

which are not tra(fe«j, so that there Is no indeterminacy in local factor prices vis a vis traded good

prices. See the Cobb-Douglas example presented in the next section for details.

Qti

small community. For convenience take p^ = 1, i.e., the export good will be

treated as the numeraire, p^, v, and w are determined endogenously in the

local market general equilibrium. Assuming for the moment that this

general equilibrium Is uniquely determined, we can view these prices as

functions of the national market prices, the demand for inputs by the big

firm, and In the short run the levels of the fixed capital input. In the short

run the endogenous factor prices are given by

(1) V = v^(PpP2, r,L^,NV^,K3) and

w = w^(p^,P2. r,LV.K^,K3), - - -^.^-—

where L° and n" are the demands by the big firm for land and labor,

respectively and K| and K-^ are the levels of the fixed capital input in the

export and locally produced good sectors, respectively. Similarly, in the

long run the endogenous factor prices are given by

(2) V = v^(p|,p2. r,L^,N^) and

w = w'(p^,P2, mV),

Suppose that the product of the big firm Is sold exclusively on the national

market and that revenues of the big firm can be taken as a function of the

Joint Inputs, (K^.L^.N^). Call this revenue function R. Our analysis does not

depend on whether R Is derived by assuming competitive or imperfectly

competitive behavior in the big firm's product market. The problem which

generates the big firm's demands for inputs Is given by

(3) maximize R(K^,L^,N^) - rK^ - vL^ - wN^.

K^,L^,N^ 2

Ourjoal IS to contrast the solutions to (3) under two alternate hypotheses.

First, the big firm acts strategically with respect to the local factor

prices. That is the big firm is a muUimarket monopsonist acting as if v and

w are given by ( 1 ) in the short run or by (2) in the long run. Second, the big

firms acts competitively with respect to the local factor prices taking v

and w as fixed.

To pursue our goal it is highly desirable that (3) admit a unique

solution. For this reason we assume that R is strictly concave. Let the big

firm's-shortTun Tnput expenditure" function, E^, be given by

(4) E^(K^,L^,N^) = rK^ + vL^ + wN^,

where v and w are given by ( 1 ). Similarly, let the big firm's long run input

expenditure function, E , be given by

(5) E^(K^,L^,N^) = rK^ + vL^ + wN^,

where v and w are given by (2). It follows that strict convexity of the Input

expe^^ture function m.G_^^r).is-a'Suff1c1ent condition for uniqueness of a

solution to (3). We will return to the conditions which ensure this

convexity. We now turn to a more detailed development of the local,

general equilibrium which generates the equations ( 1 ) and (2).

Let the local endowment of land and labor be [ and N, respectively and

let the local endowment of numeraire be m. It Is Important to note that

while factor endowments are fixed the big firm will perceive that there is

some elasticity to factor supply functions. This follows because factors

have an alternate use other than In production. That Is, consumer

a

prefernces depend on land and leisure consumption. It Is In this important

respect that our approach differs from the standard International trade

approach. Let the local utility function be denoted by U. U Is tai<en to

satisfy the standard neoclassical properties. Then the problem which

generates the consumer demands is given by

(6) maximize U(X|,X2,x-j,L,N)

X|,Xo,X3,L,N2

Subject to: X I + P2X9 + P3X3 + vL + wN = vL + wN + n|

+ n-^ + m,

where n^ denotes the profits earned in sector h for h =1 or 3. This yields

demands of the form

** i* — — —

(7) ^j

" ^j^P2^P3^^>'^'VL + wN + TT

J

+ TT-j + m) for i = 1 ,...,Z;

L^ = L^(P2,P3,v,w,vC + wN + nI

+ TT3 + m); and

^c"" N^^P2>P3^v>w,vL + wN *• TT| + rtj * m).

Let the production function in sector I be denoted by F and the production

function in sector 3 be denoted by 6. Then the problem which determines

the short run factor demands in sector 1 is given by

(8) maximize F(K |,L j,N j)- rK

j

- vL|

- wN

|

LpN^iO

This yields short run factor demands of the form

(9) l'J= l'J(v,w,K|) and N^j = n'Jcv^w^Ki).

* *.

Then, n I= F(K|,L ^,N ^) - rK^ - vL

^

- wN^.

We could proceed In a similar fashion with respect to the factor-

demands in sector 3. Since our primary concern is with the determination

of the factor prices and not with the indirect effect on the price of the

locally produced good, we will instead make a simplifying assumption which

greatly facilitates the analysis.

Assumption 1 : Capital is not used in the production of good 3. i.e.,

6(K3,L3,N3) = 6(0,L3,N3) for all K3.

Recall that we have assumed production in sector 3 is characterized by

constant returns to scale. In conjunction with assumption 1 this implies

that TT3 = 0, even in the short run. P3 will be bid up or down so that there

are normal economic profits in sector 3. That is,

(10) P3 = P3(v,w).

Thus, the purpose of assumption 1 is to reduce the number of endogenous

prices to be determined in equilibrium from three to two. Let C3 denote

the cost function In sector 3. Since It is assumed that there is no demand

for the locally produced good from outside the community it must be that

in equilibrium, P3X3 = C3(X3). Thus the factor demands in sector 3 are

given by

* ^3^3 ^ ^3^( tl ) L3 = 03(v,w) —^ and N3 =

[ 1- 03(v,w)]—^ ,

<i

where a-j(v,w) is the cost share of land in sector 3 production and

—\- a^Cv.w) Is the cost share of labor in sector 3 production.

Factor market clearing requires that

P3^3(12) L*>L%U =L!! + L%a^(v,w)^^^^^ = L - L^ and

N* *N^J

+ N3 = N^ +N^J Ml - a3(v,w)]~— = N - N^.

If the two equation system given in (12) is invertible, the inverse is then

given by ( 1 ). This completes the description of the short run local general

equilibrium.

In the long run sector 1 Just breaks even in the equilibrium prior to

the entry of the big firm. If the big firm enters at a sufficiently large

scale then local factor prices are driven up enough that sector 1 must shut

down. In this case sector 1 will revert to an Import sector just like sector

2. Then the long run equilibrium can be solved for in a similar manner to

the solution of the short run equilibrium, by assuming that production and

profit In sector 1 are both zero. Alternately, the big firm may enter at

small enough scale that sector 1 conlnues to operate, albeit at a smaller

scale. In this case the local factor prices may remain unchanged, with the

sector 1 local factor demands contracting to offset the local factor

demands of the big firm. This case is not germane to the present analysis

sine the welfare effect on the community from entry by the big firm will be

zero. Hence the community would have no Incentive to encourage the big

firm to enter In this case. It Is also possible that one local factor price Is

bid up while the other local factor price Is bid down. In genral the welfare

effects on the community are ambiguous when the factor prices move in

opposite directions. We brfefly consider this possibility in the subsequent

section.

11,2 A Cobb-Douglas Example

(n this section we develop a specific example which illustrates the

more general approach given above. Suppose

(13) U(X|,x^,x-j,L,N) = Qjlnxj + a-;,ln x>^ + ^3^^ ^3 * ^1 ^^L*^N ^^^'

where a|, 02, Oj, a^, a^ > and a

|

+ 02 + aj * «[_+ cx^ =^ • Then the

consumer demands are given by

^ vC+wN+TT|+m(14) X; =0; for i =l,...,3;

^ vL+wN+TTi+m

Lc = «L y3^^

^ vC+wN+rr|+m

Nc =^N '^^

Now suppose that the sector I production function is given by

(15) F(K|,L^,Np = K^^^L^^^N^^'^,

^ From ( 1 4) It can be seen that the purpose of the assumption that the consumer endowment

contains some of the numeraire good is to avoid the possibility that in the long run, when tt. = 0,

the consumer demands for land and labor depend only on the factor prices relative to each other

rather than on the factor prices in respect to the numeraire. See note 1

.

ta

Wherepj^, p|_, pj^

> anapj^

+p|_

+pj^

= 1. Then the short run factor

demands in sector 1 are given by"^

™l h={[i]'-»'[5?fKM"^,„0

The short run profit In sector 1 Is

Finally suppose that the sector 3 production function Is given by

(18) 6(L3,N3) = L3^N3^"^

Then the factor market clearing conditions become

( 1 9) [a^_ * a3a]

•{[^]'"''[^r"KM"^-:-L«

.[..N.„K,[a.]'^"l^]^"''^-rK,.m(a^ * a^{ I

-0)]

and

13

Ihis r^t^er-messy system of equations is nonlinear in v and w.

Nevertheless, we can still come to certain conclusions about the example.

The Long Run Case

First consider the case where Kj = 0, as will certainly be true in long

run equilibrium when the big firm enters at a sufficiently large scale. .

Then(19)simplifiesto

(20) [a|_ + a^o] = L - L^ and

f^N'^3^''^^'—;;;;

— ^^"^

(20) is linear In v and w and consequently uniquely specifies the factor

prices as functions of the big firm's factor demands, as long as the

coefficient matrix Is nonsingular. in the domain where (20) admits a

sensible economic solution, we have

[a, *a^o][N-N^]m [aM*oci( 1 -ori-L^lm'r2rT"^~ V = ^ ^

pand w= ^ ^

where D = (L - L^][N - N^] - [C - L^)N[a^ + a3( 1 -a)) - L[N - nH\ * (x^ol

Certainly C - L^, N - N^ > is required for feasibility, I.e, the big firm does

not exhaust the factor endowment In equilibrium. Then (20) admits a

sensible economic solution when D is positive. This condition puts more

stringent upper limits on the the magnitudes of L^ and N^. In this relevant

range it follows that

14

dV dV dW aw(22) ^ , ft , ^ , r1

^ ^'

dL^ dN° dL^ dN^

That is, an increase in demand for either input by the big firm bids up the

price of both inputs. Moreover, the factor prices are strictly convex

functions of the input demands by the big firm."* Since the market clearing

conditions, (20), imply that the big firm's expenditure is an increasing

aff ine transformation of the factor prices, the big firm's expenditure

function is also a strictly convex function of its input demands in this case.

Hence, when Kj = our example is amenable to the general analysis

developed in the previous section.

In order to compare the equilibrium where the big firm is a

monopsonist to the equilibrium where the big firm acts competitively it is

instructive to construct the indirect utility of the aggregate consumer as a

function of the local factor prices and then invoke the First Fundamental

Welfare Theorem. This indirect utility function, t, is given by

(23) t(v,w) = In [vL+wN-^m] - [aj_ + a^o] In v - [a^ * ^^^^ ~ ^M In w

The first paTtfats^omare given by

(24) t =-T—TT - —;;— andt^ = -:

—

tt-;;;;

•

^ vL*wN+m ^ ^ vL+wN+m ^

From (20) tt follows that t^, t^^ > as long as L^, N^ > 0. That is, as long

as the big firm is actively participating in the local factor markets,

"^ All the analytic results are given in the appendix.

^Notethota. In p. =0 since p. =1. Also note that the term - a^ In p^ is omitted in (23).

Since p^ is constant throughout the onolysis, this is just o matter of convenience.

15

welfare in the local community is an increasing function of the local factor

prices. From this it follows that the community is indeed better off by

having the big firm enter than by keeping the big firm out. Furthermore it

follows that at least one factor price must be lower in the monopsony case

than in the competitive case, because the First Welfare Theorem tells us

that the local community is worse off when the big firm acts as a

monopsonist.

Is it necessarily the case that both input demands are lower under

d^v . d^w . .. d^Emonopsony? Note that both —3

—

z and —z—;: > 0. Hence —z—;; > as

3 P nfwell. Therefore, it Is possible that ^ \ - —z—-; < Oand,

apparently, one input demand might actually be larger under monopsony than

under competition, —z—;: - —;—;; 2 for all {l^M ) is a sufficient

condition for the monopsony solution to yield less demand of both inputs by

the big firm and, hence, lower input prices.

What is the impact on the locally produced good sector from entry by

the big firm? It follows. from, C IB). tl:iat

1-0

'«' •3=erfei

Thus the price of the locally produced good rises as the big firm bids up the

local factor prices. It then follows, by substituting (25) into (1 4), that a

proportionate increase in both factor prices actually lowers the

equilibrium demand for good 3. Hence there is a tendency for sector 3 to

contract as the big firm enters, However, if the cost shares in sector 3 are

very uneven and if the big firm disproportionately bids up the price of the

factor which has the small cost share in sector 3. then it is possible for

sector 3 to expand upon entry by the big firm.

We now consider the case where K^ > after entry by the big firm.

«

That is, entry by the big firm occurs at a small enough scale that continued

operation by the old export sector is possible. Note that the average cost

function in sector \ is given by

C,(x,)

<^« ^-[mfiMg'"I SPk"* "-Pl i^n'

Since good 1 is the numeraire and since the profits in sector 1 are zero in

the long run, as long as sector 1 is In operation the local factor prices are

constrained to satisfy

(27)J.Y

In v +p|^

In w = H,

where H =pj/ In— +

pj_In

p|_ p^ In ^^. From (27) it is evident that If

one local factor price is bid up the other local factor price must be bid

down. The change in w given a unit increase in v so that (27) remains

satisfied is given by

dw ^L w(28) xw ~ ~ « ,. '

dv p,^ V

Then using (24), the welfare effect of such a price change is

17

P|_w / N 0(^*0C3(]-oX

(29) is positive if and only if

vL-[aj_+aja][vC+wN+m] wN-la^^+a-^C 1 -a)][\{]+wN+m](30)

Pl Pn

T^fe numeT<Jtm"iJT*tf!t5tef t hand side of (30) is the value of the excess supply

of land for the community, inclusive of the indirect demand for land in local

goods production but exclusive of the demand for land by either the

exporting sector or the big firm. The numerator of the right hand side of

(30) is similarly the value of the excess supply of labor. Thus the

community benefits from an increase in the price of land and a concomitant

decrease in the price of labor if and only if the ratio of the value of excess

land to labor supply exceeds the ratio of the land to labor cost shares in

sector I production.

If the local export sector continues to operate after entry by the big

firm the community will only invite the big firm in if (30) is satisfied and

the community expects the big firm to bid up the price of land or if (30) is

satisfied in reverse and the community expects the big firm to bid up the

price of labor.

Since nj

= in the long run, ( 1 9) can now be written as

/T1^ r , vC^wN^m - H ^(31) [a^ + a^a]

—

*Pl^i"^ ~^ ^^^

[Qj^ * a3( 1 -a)]

—

-— -Pf^x ^

= N - N^.

where x^ is the output of the local export sector. Observe that if the big

firm expands Its demands of both land and labor so that—;: = — and If In

dL^ Pl

dx^ -1the process the local export sector contracts its demands so that

—z = —

,

dL^ ^L

then neither local factor price is affected. That 1s, as long as the big firm

increases its local factor demands in the correct proportion, then the big

firm views the supply of local factors as perfectly elastic, regardless of —

whether the big firm acts strategically or as a price taker in the local

factor markets. Thus when the local export sector continues to operate the

following first order condition is necessary at the big firm's optimum.

(32) Pl^R^- V) + p,^(Rj^ - w) = 0.

Of course when the big firm acts competitively in the local factor markets

then both R, = v and R^ = w. When the big firm acts strategically this need

not be the case.

Note that the expenditure function E need not be convex In (L ,N ) as

long as the local export sector continues to operate. Thus we cannot rule

out multiple solutions to the big firm's problem In this case. However, It Is

not hard to show that for each output level of the local export sector, Xj,

there Is a unique (v,w) pair which satisfies (27), (3 1 ), and is profit

maximizing for the big firm.

Short Run Analysis

19

.

Obviously we cannot obtain an explicit analytic solution for the

-factor prices given by ( 1 9) when K| > 0. Nevertheless In the region where

(19) adnaits an economic solution this solution Is unique.^ Moreover it is

still the case that.

,^-„ dv aw(33) ~d ' ~d > 0.

dv dwHowever, in the short run it is possible that

—-z ,—z < 0. In the long run

case bidding up the price of one Input raises the local demand for the other

input via Income effects. In the short run this effect is still present but

the demand for the other input in the export producing sector is reduced.

The export producing sector is squeezed by the increase in factor demand

from the big firm and responds by a decrease in its own factor demands.

Hence the overall effect on the local demand for the other input Is

ambiguous. Convexity of the factor prices in the big firm's factor demands

is still a sufficient condition for convexity of the the big firm's

expenditure function. Finally, the local community's welfare is increasinjg

in the local factor prices given that the big firm is taking a positive

position in the local factor markets. Thus the same caveats concerning the

monopsony solution in the long run case are also applicable to the short run

analysis.

^ Apart from restrictions on the size of the big firm's factor demands it Is necessary that the level

of the fixed ijapltd) input In the export producting sector not be too large. By limiting the size of

the fixed cost In this sector positive net wealth of the community can be ensured.

20

IN. An Intertemporal Approach

While the static model developed in the previous section is an

improvement on the partial equilibrium approach to monopsony, it appears

somewhat at odds with some stylized facts concerning the way local

communities in the United States appear to woo large firms. Casual

empiricism suggests that small communities try to attract large firms

because they expect a substantial boon to local employment and because

they also anticipate a concomitant increase in local land values. While the

static long run model predicts increases in both factor prices relative to

the preentry equilibrium, the strategic behavior by the large firm

seemingly mutes these effects. Yet recently it appears that big firms often

pay the national Industrial wage upon entry into a small community. If this

is correct then this fact would appear to be at odds with the predictions of

our static model.

Recent theories concerning "efficiency wages" may explain why the

big firm finds it advantageous to pay such high wages when it possesses

monopsony power7 But if we are to rely on efficiency wage theory to

explain the high wages offered by the big firm, and note that the local

reservation wage is likely to be substantially lower than the urban

reservation wage even after entry by the big firm, then there is only the

land market In which the big firm can exercise its strategic power. But as

we have already noted, there is the anticipation that local land values will

rise substantially as well. We believe that there is something else going

i

^ For a good survey of the efficiency wage literature see the volume edited by Akerlof and Yellen

(1986).

21

here. Below we provide a possible explanation consistent with these

stylized facts. ~

Our point of departure Is In the assumption that the big firm has

better access to credit markets than does the local community. This

assumption, together with the knowledge that local factor prices will rise

as a consequence of its entry, provides the big firm with an incentive to act

as an arbitrageur in the land market. That is, prior to the time that the big

firm has established its operation in the local community, the big firm buys

up land in excess of what is needed for its operation. Once its operation

has been fully established and local factor prices have been bid up as a

consequence, It sells back the excess land to the community and thereby

earns a handsome profit

If this channel for excercising strategic power is open to the big

firm then the big firm should base its location choice, in part, on the

community's access to credit, preferring more isolated unknown locations.

Moreover, if the land market is vertically integrated with the local goods

and services market then this form of arbitrage will take the form of the

big firm becoming a signifigant pjayer in local industry. In other words,

this theory is consltent with the notion of the development of a company

town.

To get an idea of how this arbitrage works consider an infinite

horizon, discrete time model. Suppose that In each period the model is

similar to the static model developed in section II. 1 That is, the utility

function, U, is now to be Interpreted as the per period utility function and

22'

time preference for the community is determined by the discount rate 5.8

In the period prior to its operation the big firm buys up land iTTthe~

community but does not participate in the local labor market. Assume that

in all subsequent periods the big firm is in operation and a stationary

equilibrium is established.^ The per period equilibrium of all periods but

the interim period, in which the big firm buys up land, is described by the

static model we have already developed with the exception that the

community's endowment of land is now net of what it sold to the big firm in

the interim period and the big firm now may be a supplier rather than a

demander of land.

Let Vg be the stationary equilibrium rental price of land and let i^ be

the long run interest rate in the community. Then the stationary

equilibrium land price, p^, is given by

(34) Ps— ^S-

Similary, the interim equilibrium price of land in the community in the

period when the big firm buys up land, Pj, is given by

Ps ^*^ ^S^^5^ Pi=^r M;=^r 7^17^

Q This Intertemporal additive separability of preferences implies zero intertemporal cross price

effects In demand, which greatly facilitates the analysis.

^ This requires that the long run interest rate which the community faces equals the community's

rate of time preference.

23

where Vj is the rental price of land and ij is the short run interest rate in

the interim periodJ^'^^s

^^l

^^cause the big firm's demand for labor is—

sufficient to bid up the price of land in the long run, more than offsetting

the arbitrage in the land market by the big firm, then there is a capital gain

in land as long as ij i ic. We take this as our starting point.

Assume that consumers in the local community have rational point

expectations as to the long run equilibrium prices once the big firm is in

operation. The question which concerns us here is how does strategic play

by the big firm once it is in operation impact on the price of land in the

interim period? In particular, for a given level of land purchased by the big

firm in the interim period, how does an increase in the big firm's long run

demand for labor or a decrease in its supply of land affect P|? It turns out

that P| is likely to be inelastic with respect to such strategic moves by the

big firm and to be more inelastic the smaller is the community's elasticity

of credit.^ 1

Consider the extreme case where all loans in the community are

self-financing, so that in the absence of entry by the big firm the

community must maintain balanced trade with the rest of the world. We

will show that In this extreme case such strategic play by the big firm has

no effect at all on V|. Let L^ denote the amount of land bought up by the big

firm in the interim period Then the stationary equilibrium with the big

firm In operation is determined by the same set of equations that we have

I ^ Since we are abstracting from any considerations of risk , the short run interest rate will

depart from the long run interest rate only if the community's supply of credit is imperfectly

elastic.

'' Of course, when the supply of credit to the community is perfectly elastic the anticipated

increase of the land rental price will bid up p. substantially. In this case, p^ will exceed p. only

by the difference between v^ and v..

24-

already examined In the static model, with the exception that the

comrriunttg's endowment of land In this stationary equilibrium Is given by

C -L J and the big firm may very well be a net supplier of landJ^ since

there are no Intertemporal cross price effects In demand, the local

community's demand for land and labor services In the Interim period Is a

function of the exogenously given prices of the Imported and exported

goods, the Interim period rental prices, Vj and Wj, as well as the lifetime

1+iq WqN+mwealth of the community, P|C + WjN + m + t— —:

=

"^^" Ulq VqL+WcN-^mVjL + WjN + m + Tj-j- : . Moreover, given our restriction on

preferences, there is a unique pair of factor prices and level of community

wealth which gives rise to a given land and labor demand pair. Now

suppose In the interim period consumers In the community rationally

antlcpate a long run Increase in the big firm's demand for labor but witness

no change In the amount of land the big firm buys up In the Interim period.

This Increase In labor demand will bid up w^ and v^. However, from the

above V| and W| should remain unchanged Thus, in this extreme case ij

adjusts so that the community perceives no Increase in Its lifetime wealth.

In other words, in this extreme case rationally anticipated changes in the

big firm's stationary equilibrium behavior will have no effect on the

Interim rental prices. Such changes will manifest themselves only through

the changes In the short run Interest rate. Indeed, If v^and l+ij Increase In

the same proportion then there is no change In p, whatsoever.

'- This would be the case If the amount of land t)ought up In period I exceeds the Pig firm's use of

land In production.

25

The point here is that in deciding on its optimal strategic play once it

has obtained full operationthe big firm can more or less ignore the impact

this play has on its preentry price of land. Since in the long run

equilibrium the big firm is operating as a monopsonist in the labor market

but as a monopolist in the land market it is quite conceivable that the long

run wage is competitive or even supercompetitive and that land prices are

quite high.

IV. Conclusion

In this paper we have been concerned with developing a general

equilibrium framework for analyzing the impacts of entry by a large firm

into a small community which is consistent with the notion that

communities bid to attract such firms because they generate substantial

income locally. Far from feeling that we have offered a complete analysis,

we hope that our paper will stimulate further work in the area. Below we

present some points in which the current analysis is deficient and which

might prove fruitful for study.

First, this paper completely Ignores the effects of labor migration

Into the community from adjacent areas. Such effects are obviously of

great Interest to regional scientists. Moreover, reconciling such migration

with the fact that big firms pay high wages Is all the more perplexing

because It would seem that the such labor migration would make the big

firm's labor supply more elastic than is suggested by the analysis in this

paper.

Second, other channels apart from different access to credit markets

should be explored in regard to the big firm's ability to act as an

arbitrageur in the land market. In this paper we have ignored the fact that

prior to entry by the big firm, the local community is typcially in

competition with other communities for the plant that the big firm will set

up. Such competition may lend an air of uncertainty which is absent in our

model. Is it conceivable that the big firm can utilize this uncertainty of its

location choice to aid it in land speculation?

Finally, we have not addressed the issue of community size. In other words,

in the static framework a sensitivity analysis on how the big firm's profits

vary with the basic parameters of our model would be of great interest.

Furthermore, while we have argued that the big firm would like to enter a

community which has limited access to credit markets in the intertemporal

model, obviously the big firm would prefer that its labor supply is

plentiful. An examination of how this tradeoff affects the big firm's

location choice would also be highly desireable.

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I

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i.

Appendix on Cobb-Douglas ExampleI

Long Run Analusls

Since D = [L - L^][N - N^] - [L - L^]N[aj^ ^ a3( I -a)] - C[N - N^jfa^ - a^o] and

since C - L^. N - N^ > 0. It follows that

.d_M r-id.nN - N" - NlQj^ * 03(1-0)] > and L - L^ - L[a|_ * 030] >

are necessary conditions for D > 0. Then the precise comparative static

results are

(3V V - r» -—j= p{N-N'^-Nla,>j + a3(l-a)l}>0 and

av_ V .[L-L^]N[a,^*a3(l-o))

dN N-N"^}>0

Next we can optain the second partials as follows

d^v= 2— {N - N^ - N[aK, * aM-o)])^ > 0,

dLd2 D^^ "^N--3^

a^v y^Nia^+a3(l-a)]

dL^aN^"dI

N-N'}

2 -^ {N-N^-N[a^ - a^{ 1 -o)])[ r^ ) >

J

{N-N^-N[a,^*a3(l-a)]rL-L^]

because g > 1 , and

Moreover, —2—2 "L ~~d~~d J

"

-7 {N - N^ - NlQj. - a^C 1 -o)]f ( r-V? 1-

^v^MM(1M^ n r [L-L^]N[a^>a3(]-a)] ^^N[a^>a3(i-a)]

^ _

3^ {N-N^-N[a, ^ a3( 1 -a)]}{ rV ) ( . . d 1

:l-l^]ni

^2^[[-L^]N[a;^^a3(l-a)]

^

1D

1 ^1^ )) ' ^N-N^

{N-N^-N[a^j>a3(l-a)]rL-L^]

where the last Inequality follows because ^

I!

and

N[aj^+a3(l-a)]

N-N^ < 1. This demonstrates that v is strictly convex and

increasing in the big firm's factor demands when these factor demands are

in the relevant range. Since the equilibrium is symmetric the same results

also apply to w.

Short Run Analysis

The market clearing conditions (19) can be rewritten as

[a^ + a^o]

vL+wN+n,+mJt _ H

+ L 1 = L - L° and

vL+wN+TTi+m ^ _ H[a,^ * a^{\ -0)1 ^;p^— - N^ = N - N^.

Existence of a solution follows by standard arguments since the demands

are well behaved. For uniqueness of a solution consider the Jacoblan of this

system

-[a|_+a3a][vL|+wN+n|+m] dL«. )i

[a|_+a3a)[N-N|] dL

dv dw

*, *»

[aj^+a3(l-a)]|C-L|] dN| -[a|^+a3(l-o)]lv{.+wN|+nYm) dN|

w dvW"

dw

This Jacobian is nonsingular. Indeed the matrix is negative definite since

it is the sum of

-[a|_+a3<7l[vL ^+wN+Tr|+m]

w

laL+a3a]lN-N^]

[a,^+a3( I -a)]C-L*l "t<^M''^3^ ^ -a)][\{.+wN'J+TT ^+m]

w

and

dL^ dL

dv dw

dN| dH

L dv dw J

both Of which are negative definite. This implies that each solution is

Isolated, it also implies the comparative statics results suggested in the

text In (25).

Next consider the function H given by

H(v,w) = ML - L^] - [a|_ * a^o] [vC ^ wN + tT| + ml - vL^J)^*

{w(N - N^l - [a,^ * a3( 1- ^)1 [vL + wN * TT

J

+ mj - wN*}^.

Note that from (1 6) and (17) it follows that tT|, vL|, and wN^ are all

strictly concave in (v,w). Hence H(v,w) is convex in (v,w). Moreover for v/

fixed H explodes as v approaches either or <». Similarly for v fixed H

explodes as w approaches either or <». it follows that H attains its

minimum over the first quadrant at some strictly positive (v,w) Moreover,

the set of such minimizers must be convex, in fact any solution to ( 1 9) must

V

be such a minlmlzer of H because H Is obviously nonnegative and is zero at a

solution to (I9X It follows that the solution to ( 19) is unique.

i